Is Barack Obama’s duty to hear the voices of the entire country or is it to heed the entreaties of his allies on the left and in the Democratic Party?

That is one of the simplest, and also one of the most complex, questions of our time. To ask it is to please conservatives who argue that Mr. Obama consistently ignores their impulses and ideas. To answer it pleases liberals who want to believe that their impulses and ideas are squarely in the national interest.

Here’s the ideal: As a nation, the American people select only two office holders, the president and the vice president. These are the only officials who represent the entire country, the only two whose remit is the national interest. Senators have home states to speak for, House members have districts, and among them they act for interests rural or urban, industrial or agricultural.

Here’s the reality: The principle of national representation in the presidency is honored only in the breach, and usually briefly.

Franklin Delano Roosevelt spoke for the whole country in his “fear-itself” inaugural address and, given the magnitude of the economic crisis, probably in the first hundred days of his administration. But as the New Deal turned left, FDR increasingly spoke a language congenial to liberals, which is why he sometimes was considered a traitor to his own class.

In the days after Sept. 11, 2001, George W. Bush spoke for the nation, but as the shock of the terrorist attacks wore off, he was vulnerable to criticism that he had become the servant of conservative and business interests and the enemy of civil liberties.

Mr. Obama came to office on a flood of hopes for racial reconciliation and on a jet stream of rhetoric about changing the way Washington works by creating a post-partisan political system. But his early priority, along with an economic stimulus, was a comprehensive overhaul of the health care system — an issue arguably more important to Democratic activists than to Mr. Obama as a state senator and U.S. senator.

Much of the president’s past year has been spent going it alone, especially in recent weeks as he has refined his immigration initiative. That tactic will be substantially more appealing, and substantially more difficult, in January, when the new Congress with its twin Republican majorities is seated.

Perhaps that is why he was so fulsome in his praise of the flawed but efficient spending agreement sculpted on Capitol Hill earlier this month. Listen to his comment as the measure neared completion:

“This by definition was a compromise bill. This is what is produced when you have a divided government that the American people voted for. Had I been able to draft my own legislation, get it passed without any Republican votes, I suspect it would be slightly different.”

But Mr. Obama acknowledged that “what the American people very much are looking for is responsible governance and the willingness to compromise.”

And yet two conditions conspire against compromise.

The first is the spirit of the age, which considers compromise morally empty and which rewards, in television appearances and in fund-raising entreaties, uncompromising conviction.

The other condition is the end of the old politics, which featured a Republican Party with moderates and a Democratic party with conservatives — conditions that shaped the Lyndon Johnson and Richard Nixon presidencies, both highly productive, though also controversial. Indeed, a substantial number of Republicans voted for Mr. Johnson in 1964 and a substantial number of Democrats voted for his successor, who had a “Democrats for Nixon” branch of his 1972 re-election campaign.

Richard Skinner, an imaginative political scientist at American University, has developed a theory that presidents disproportionately represent the people who elected them — a trend that has historical antecedents but clearly is in the ascendancy today.

“Presidents tend to pursue the parties that they come from and interests and ideas that are strong in their party,” Mr. Skinner argues. “That is even stronger today than in the past, because it is so hard today for presidents to get support either in Congress or from the voters from the other party.”

Though Bill Clinton oftentimes leaned rightward — with the overhaul of the welfare system, for example — the last great practitioner of the politics of compromise was George H. W. Bush, who disavowed “the vision thing” but had a broad national vision.

Mr. Bush paid for that in the rebellion against the 1990 bipartisan budget deal that propelled Newt Gingrich into prominence and undermined the president’s support within his own party.

The 41st president had strong partisan, and even stronger competitive, impulses. No presidential candidate of the modern era ran as disciplined and combative a campaign as Mr. Bush conducted against Michael S. Dukakis. With remorseless rhetoric and a brutal television offensive, Mr. Bush pummeled the Massachusetts governor, who at one point had a 17-point lead over the vice president.

Yet shortly after Mr. Bush took the oath of office, he delivered an inaugural-address critique of the nation’s politics that is eerily similar to that of our own, except in recent years things have grown only worse: “We have seen the hard looks and heard the statements in which not each other’s ideas are challenged, but each other’s motives. And our great parties have too often been far apart and untrusting of each other.”

Then the new president, addressing Jim Wright of Texas and George Mitchell of Maine, the top Democrats in the House and Senate, respectively, said: “I put out my hand. I am putting out my hand to you, Mr. Speaker. I am putting out my hand to you, Mr. Majority Leader. For this is the thing: This is the age of the offered hand.”

Today we don’t even have the iron hand in the velvet glove that Napoleon spoke of but, instead, the iron hand in an iron glove.

Perhaps combatants of both parties, and the president himself, might review Mr. Obama’s first inaugural address, delivered in 2009. In those remarks, the new president — then still full of hope, then still with the capacity to make his rivals shake in fear — said, “What is required of us now is a new era of responsibility — a recognition, on the part of every American, that we have duties to ourselves, our nation and the world.”

Those are words to remember. They are also words to live by, both on Capitol Hill and in the White House.

David Shribman, a Pulitzer Prize winner in journalism, is executive editor of the Pittsburgh Post-Gazette.